ImagingImaging

PETPET

Course LayoutCourse LayoutClassDateClass + Content

I23.2.2005Physical Principles of PET

II2.3.2005Physical principles of MRI

III9.3.2005Imaging applications

IV16.3.2005Image Reconstruction PET and MRI

V23.3.2005Automatic Image Alignment

VI30.3.2005PCA

VII6.4.2005No Class

VIII13.4.2005GLM

IX4.5.2005GLM relation to classical tests (Anova, T-test..)

X18.5.2005Covariates

XI25.5.2005Gaussian fields Theory

XII1.6.2005Specific experiment design and analysis

XIII8.6.2005Specific experiment design and analysis

XIV15.6.2005Correction for multiple measurements

Talk LayoutTalk Layout SPECT (Short introduction)SPECT (Short introduction) PET – Physical principles and PET – Physical principles and

StructureStructure PET correctionsPET corrections PET image reconstructionPET image reconstruction PET Typical applications in Brain PET Typical applications in Brain

ScienceScience

Principle of radionuclide Principle of radionuclide imagingimaging

Introduce radioactive Introduce radioactive substance into bodysubstance into body

Allow for distribution and Allow for distribution and uptake/metabolism of uptake/metabolism of compoundcompound Functional ImagingFunctional Imaging!!

Detect regional variations Detect regional variations of radioactivity as of radioactivity as indication of presence or indication of presence or absence of specific absence of specific physiologic functionphysiologic function

Detection by “gamma Detection by “gamma camera” or detector arraycamera” or detector array

(Image reconstruction)(Image reconstruction)

Single photon emission Single photon emission CT (SPECT)CT (SPECT)

Single photon counting:Single photon counting: Windowing (reduces scatter, Windowing (reduces scatter,

background)background) Counting statistics limited Counting statistics limited

by patient radiation doseby patient radiation dose ~ 30 min examination w/ ~ 30 min examination w/

cameracamera First SPECT 1963 (Mark First SPECT 1963 (Mark

IV) used array of detectorsIV) used array of detectors Rotation, TranslationRotation, Translation High count ratesHigh count rates Many componentsMany components Mostly single-sliceMostly single-slice

Rotating camera:Rotating camera: Multiple slicesMultiple slices Multi-camera systems Multi-camera systems

SPECT applicationsSPECT applications Brain: Brain:

Perfusion (stroke, Perfusion (stroke, epilepsy, epilepsy, schizophrenia, schizophrenia, dementia [Alzheimer])dementia [Alzheimer])

TumorsTumors Heart:Heart:

Coronary artery Coronary artery diseasedisease

Myocardial infarctsMyocardial infarcts RespiratoryRespiratory LiverLiver KidneyKidney

PETPET

Positron emissionPositron emission

Scintillation DetectionScintillation Detection

1-to-1 CouplingExcellent livetime characteristics, but expensive, and limited in size to smallest available PMT (~1cm2).

Block DetectorIndividual crystals “pipe” light to detectors.More complex, but required with low light output

Anger CameraLight from scintillator is distributed among several PMT’s; measured distribution determines location.Poor livetime, but can have good resolution with enough light output--NaI(Tl).

Detector AssembliesDetector Assemblies

Block DetectorBlock Detector

PET evolutionPET evolution

PETPET

Coincidence DetectionCoincidence Detection

DET 1 DET 2

Pulse Processing

AND

Pulse Processing

CoincidencesCoincidences

Coincidence EventsCoincidence Events

1

1. Detected True Coincidence Event

2

2. True Event Lost to Sensitivity or Deadtime

3

3. True Event Lost to Photon Attenuation

4

4. Scattered Coincidence Event

5a 5b

5a,b. Random Coincidence Event

Accidental (random) Accidental (random) coincidences:coincidences:

Two unrelated annihilation photons reach two Two unrelated annihilation photons reach two opposing detectors within the time window of opposing detectors within the time window of the coincidence resolving time the coincidence resolving time (~10-20 ns)(~10-20 ns)

detector i

detector j

1

2

D d

2Aij i jC f C C

: Pulse legth (2 = resolving time)f : Fraction of detectors involved f ~ 1 Ci,Cj: Individual (single) count rates

Attenuation CorrectionAttenuation Correction

0 0

( ') ' ( ') ' ( ') '

1 2

x R R

x

x dx x dx x dx

p p p e e e

Scatter EliminationScatter Elimination

Filtered Back ProjectionFiltered Back Projection

FilteredFiltered B Baack Projectionck Projection

Filtered Back Projection

Filtered backprojection• Filter the measured projection data at different projection angles with a special function.• Backproject the filtered projection data to form the reconstructed image.

Filtering can be implemented in 2 ways, in the spatial domain, the filter operation is equivalent to to convolving the measured projection data using a special convolving function h(t)

p t p t h t, ( , ) ( , ) ( )

More efficient multiplication will be in the spatial frequency domain.• FFT the measured projection data into the frequency domain:p(,)=FT {p(t, )• Multiply the the fourier transform projections with the special function.•Inverse Fourier transform the product p’(,).

2D Vs. 3D2D Vs. 3D

RandomsRandoms

ScattersScatters